Hong Kong's airport has cancelled flights for a second day as pro-democracy protesters again peacefully demonstrate in the main terminal.

Key points:

Tuesday marks the fourth day of protests at the airport, which is one of the world's busiest

Flights were also cancelled on Monday but the airport reopened on Tuesday morning

The airport's authority has advised the public not to come to the airport

Check-in services for departing flights were suspended as of 4:30pm on Tuesday (local time), but the airport's authority said it did not expect arriving flights to be affected despite dozens of arrivals already being cancelled.

Most protesters had left the airport shortly after midnight, with about 50 still there on Tuesday morning when the airport reopened; however, by the afternoon several hundred had returned, responding to a call for a new rally.

Tuesday marks the fourth day demonstrators have taken to the airport calling for democratic reforms and an independent inquiry into police conduct.

Increasingly violent protests over the past two months have plunged the Chinese-ruled city into its most serious crisis in decades and presented a serious challenge to Beijing.

Authorities have arrested more than 600 people since the rallies began in June.

The ABC spoke to passengers at the airport. Two of them were newlyweds on their honeymoon trying to get home to London.

The People's Daily, the official newspaper of China's Communist Party, posted on Chinese social media a statement saying the People's Armed Police were in Shenzhen prepared to handle "riots, disturbance, major violence and crime and terrorism-related social security issues".

It is not clear when the video was filmed.

Hu Xijin, the Global Times' Chinese editor-in-chief posted on his Weibo account that the protesters were "asking for their own death".

Protesters say they are fighting against the erosion of the "one country, two systems" arrangement enshrining partial autonomy for Hong Kong when China took it back from Britain in 1997, and have shown no sign of letting up on their campaign.

The protests were initially sparked by a now-abandoned extradition bill that would have allowed criminal suspects to be sent back to mainland China.

The city is on edge after more than two months of near-daily and increasingly bloody confrontations between protesters and police.

Protesters pushing Hong Kong 'into the abyss', Lam says

Protesters say police have used excessive force, firing tear gas and bean bag pellets at close range, and are calling for an independent inquiry into the crisis.

An emotional Ms Lam, who appeared to be fighting back tears, told reporters at a media conference that dialogue would only begin when the violence stopped and questioned whether the protesters were "hardhearted enough to push Hong Kong into the abyss".

Hong Kong's leader reiterated her support for the police and said they have had to make on-the-spot decisions under difficult circumstances, using "the lowest level of force".

"After the violence has been stopped … I as the chief executive will be responsible to rebuild Hong Kong's economy … to help Hong Kong to move on," Ms Lam said.

She did not elaborate on what steps her government would take toward reconciliation and dodged questions on whether she had the power to withdraw the controversial extradition bill.

Travellers put off Hong Kong

Kerry Dickinson, a traveller from South Africa, said she had trouble getting her luggage on Tuesday morning.

"I don't think I will ever fly to Hong Kong again," she said.

Ms Lam's comments come after China said the anti-government protests that have swept the city over the past two months had begun to show "sprouts of terrorism".

"That's certainly not the rhetoric that I would use to describe those events," he said.

"Of course we're concerned, particularly because of the number of Australians, residents and citizens, that are in Hong Kong both on a long-term basis and a short-term basis."

Mr Morrison said Australian consular officials were urging calm in Hong Kong, and offering assistance to Australia citizens and residents in the region.

He said Hong Kong's chief executive should be "listening carefully to what people are saying in Hong Kong and work towards a peaceful and calm resolution of what is a very, very serious issue".

China said on Monday that the protests had reached a "critical juncture", however, some legal experts say the official description of terrorism could lead to the use of anti-terror laws.

The increasingly violent demonstrations have plunged the Chinese-ruled territory into its most serious crisis in decades, presenting Chinese leader Xi Jinping with one of his biggest challenges since coming to power in 2012.

Hundreds of flights still affected

Despite the airport reopening, Hong Kong's flagship carrier Cathay Pacific Airways said it had cancelled more than 200 inbound and outbound flights, according to its website.

The airport — one of the world's busiest, handling 73 million passengers a year — blamed demonstrators for halting flights on Monday, but the exact trigger for the closure was not clear as protesters occupying the arrivals hall for the past five days have been peaceful.

"The [handling] of last night was chaotic," said Australian Kate Flannery, who was travelling to Paris.

"The airport authority didn't deal with the situation. I felt like I was walking around and nobody gave us information."

A Cathay customer officer at the airport, who declined to provide his name, said that nearly all of the airline's flights were full.

Adding to the protesters' anger, the chief executive of Cathay Pacific Airways told employees in a memo that the carrier has a "zero tolerance" for employees joining "illegal protests" and warned violators could be fired following a warning from Beijing that represented an escalation into the territory's business affairs.